Thermal noise in GW detectors How much can an object be at rest on Earth?

1. Thermal noise in GW detectorsHow much can an object be at rest on Earth? Geppo Cagnoli cagnoli@fi.infn.it INFN - Firenze University of Glasgow ITIS Citta’ di Castello UTB - Physics & Astronomy - 16 Sept. 2009

2. Fixing the problem • Earth is not an inertial • reference frame • Tidal effects • Geological movements Time scale or frequency range has to be defined 1Hz to 10 kHz UTB - Geppo Cagnoli - Thermal noise in GW detectors

3. Limiting the range 10 orders of magnitude We could live the object on a table but the Earth is noisy Uncertainty Principle DEDt = h / 4p For a 10 kg mass: UTB - Geppo Cagnoli - Thermal noise in GW detectors

4. Mechanical Filteringof the Seismic Noise Possible improvements Connected to ground A simple pendulum provides a good filtering above the resonant frequency y • Use a spring to filter the • vertical noise too • With a multiple pendulum configuration is possible to fill the10 orders of magnitude • We could use some damper to reduce the resonant peaks Object x UTB - Geppo Cagnoli - Thermal noise in GW detectors

5. Virgo Superattenuator THE REFERENCE POINT !! UTB - Geppo Cagnoli - Thermal noise in GW detectors

6. The Brownian motion In 1832 the botanist Robert Brown observed a random motion of pollen and dust grains suspended in water Botanist Robert Brown, (1773-1858) A challenge for the audience: how would you establish that this endless motion is not due to the activity of living organisms? 2 micron particles in water (left) and in concentrated DNA solution (right), 4 s of data http://www.deas.harvard.edu/projects/weitzlab/research/brownian.html UTB - Geppo Cagnoli - Thermal noise in GW detectors

7. Einstein’s Insight of 1905:A Way to Measure kB Einstein’s specific prediction: in pure water at temperature 17o C (290 K or 63o F), a particle of diameter 1 mm will move an average horizontal distance equal to 6 mm in one minute. UTB - Geppo Cagnoli - Thermal noise in GW detectors

8. Is Einstein famous for Relativity? UTB - Geppo Cagnoli - Thermal noise in GW detectors

9. Random motion also in mechanical systems R.K.Pathria Statistical Mechanics Pergamon Press Reducing the air pressure, the r.m.s. motion doesn’t change but the lower trace is almost monochromatic whereas the higher is more random It MUST vibrate ifthe equipartitiontheorem is right ! <E> = kT/2 for each d.o.f. UTB - Geppo Cagnoli - Thermal noise in GW detectors

10. Non equilibrium thermodynamics • Non isolated system shows uncorrelated fluctuations of volume and temperature • Two independent fluctuating variables: T, V system UTB - Geppo Cagnoli - Thermal noise in GW detectors

11. Some comments • EASY TO JUSTIFY MECHANICAL VIBRATION FROM VOLUME FLUCTUATION • RESIDUAL GAS EFFECT IS HARD TO BE IMPLEMENTED • NO SPECTRAL INFORMATION FROM THE PREVIOUS RELATIONS UTB - Geppo Cagnoli - Thermal noise in GW detectors

12. The Fluctuation-Dissipation Theorem - 1 • H.B. Callen and T.A. Welton, Phys. Rev. 83, 34 (1951) • R Kubo 1966 Rep. Prog. Phys.29 255-284 • It applies to linear systems in thermal equilibrium • It is used to predict the level of thermal noise of one observable x of the system  F(t) X(t) Linear system UTB - Geppo Cagnoli - Thermal noise in GW detectors

13. The Fluctuation-DissipationTheorem - 2 • It gives the amplitude of the fluctuations of force Sff(w) that is shaking the system, at each angular frequency w • As seen in the experiments, the noise spectrum is shaped by the “friction” v(w) SPEED Coefficient ofviscosity = g(w) = = F(w) FORCE UTB - Geppo Cagnoli - Thermal noise in GW detectors

14. Direct 2 variables are fluctuating Intuitive The spectrum is hard to extract Indirect Dissipation replaces fluctuation Not intuitive Extremely powerful for noise level prediction: is “easy” to measure g(w) The double approachto thermal noise UTB - Geppo Cagnoli - Thermal noise in GW detectors

15. Our system • 20 to 40 kg silica mirror • Suspended by 4 fibres • Dielectric coatings applied on the front faces for maximizing or minimizing reflection • The reference is the mass front face, where the laser beam senses the position UTB - Geppo Cagnoli - Thermal noise in GW detectors

16. Volume fluctuations in solids • The volume fluctuations (as the thermal ones) need to fulfil the boundary conditions • Perfect solids (crystals) vibrates at their resonant frequencies • The real solids have defects that move or change driven by the finite temperature of the solid: • The vibration has a continuous spectrum rather than a discrete one • NO DIRECT METHOD APPROACH: • Mechanical losses of materials are investigates and thermal noise level is worked out through FDT UTB - Geppo Cagnoli - Thermal noise in GW detectors

17. How to measure the mechanical loss t A0 A0/e A method widely used is to detect the free decay of the excited resonances of the system In order to know the frequency distribution of noise, the viscosity constant g has to be measured at all the frequencies of interest UTB - Geppo Cagnoli - Thermal noise in GW detectors

18. A new sample holding systemGeNS Vacuum tank Sample Sapphire half sphere Dr. Elisabetta Cesarini UTB - Geppo Cagnoli - Thermal noise in GW detectors

19. The most severe limit for IFOs:thermal noise from the coatings • Alternate layers of transparent materials with different index of refraction • Impedance mismatch andinterference produce highcoefficient of reflectivity • Its structure is not compact as the substrate • 10 mm of coating produces morethermal noise than 10 cm of substrate UTB - Geppo Cagnoli - Thermal noise in GW detectors

20. Thermoelastic noiseEffect on suspension fibres - 1 de = a·dT Asymmetrical thermal fluctuations are responsible of thermoelastic noise on silica fibres (DIRECT APPROACH) In linear thermoelastic effect thermal expansion coefficient a transforms thermal fluctuations in strain fluctuations Fibres bend and then the suspendedmass is shaken. The effect is small butrelevant in GW detectors Same kind of deformations occur in mirrors UTB - Geppo Cagnoli - Thermal noise in GW detectors

21. Thermoelastic noiseEffect on suspension fibres - 2 • The heat transfer sets a characteristic time scale that makes the noise spectrum frequency dependent, like: Debye peak: Noise or friction intensity • Fused silica facts: • Low a • Low g • High strength frequency UTB - Geppo Cagnoli - Thermal noise in GW detectors

22. Fused silica fibre productionand testing • The CO2 laser pulling machine was developed in Glasgow • The machine was financed by EGO as well as PPARC and in 2006 it was delivered to Pisa • The machine was then adapted to the Virgo necessities and thanks to the excellent work of Dr. Matteo Lorenzini, Francesco Piergiovanni, Dr. Filippo Martelli, Virgo now has fused silica suspensions of high precision and strength UTB - Geppo Cagnoli - Thermal noise in GW detectors